1. Solving Equations by Factoring
Definition of Quadratic Equations
Zero-Factor Property
Strategy for Solving Quadratics

3. Standard Form Quadratic Equation
Quadratic equations can be written in the form
ax2 + bx + c = 0
where a, b, and c are real numbers with a  0.
Standard form for a quadratic equation is in descending order equal to zero.
BACK

4. Examples of Quadratic Equations
Standard Form
BACK

5. Zero-Factor Property If a and b are real numbers and if ab =0, then
a = 0 or
b = 0.
BACK

6. Solve the equation (x + 2)(2x - 1)=0
By the zero factor property we know...
Since the product is equal to zero then one of the factors must be zero. OR
BACK

7. Solve the equation. Check your answers.
Solution Set OR
BACK

8. Solve each equation. Check your answers.OR
Solution Set
BACK

9. Solving a Quadratic Equation by Factoring
Step 1 Write the equation in standard form.
Step 2 Factor completely.
Step 3 Use the zero-factor property. Set each factor with a variable equal to zero.
Step 4 Solve each equation produced in step 3.
BACK

10. Solve.
BACK

11. Solve.
BACK

12. Solve.
BACK

13. Number Of Solutions
The degree of a polynomial is equal to the number of solutions.
Three solutions!!!

14. Set each of the three factors equal to 0.
Example
x (x + 1)(x – 3) = 0
Set each of the three factors equal to 0.
x = 0
x + 1 = 0
x – 3 = 0
x = -1
x = 3
Solve the resulting equations.
x = {0, -1, 3}
Write the solution set.
BACK

15. Solve.
BACK

16. x2 – 9x + 20 = 0 (x – 4)(x – 5) = 0 x – 4 = 0 x = 4 x – 5 = 0 x = 5
Example:
Standard form already
Factor
Set each factor = 0
Solve
Write the solution set
BACK

17. 4x2 – 49 = 0 (2x + 7)(2x – 7) = 0 2x + 7 = 0 2x – 7 = 0 Example
Standard form already
Factor
Set each factor = 0
Solve
Write the solution set
BACK

18. Solving Equations
Now that we know how to factor, we can apply this knowledge to the solution of equations.
How would you solve the following equation?
x2 – 36 = 0
Step 1: Factor the polynomial.
(x - 6)(x + 6) = 0

19. Solving Equations
Step 2: Apply the zero product property which states that
For all numbers a and b, if ab = 0, then
a = 0, b = 0, or both a and b equal 0.
(x - 6)(x + 6) = 0
Therefore (x – 6) = 0 or (x + 6) = 0.
x + 6 = 0
x – 6 = 0 or
x = 6
x = -6
This equation has two solutions or zeros: x = 6 or x = -6.

20. x2 – 25 = 0 x2 + 7x – 8 = 0 x2 – 12x + 36 = 0 c2 – 8c = 0 You Try It
Solve the following equations.
x2 – 25 = 0
x2 + 7x – 8 = 0
x2 – 12x + 36 = 0
c2 – 8c = 0

21. Summary of Steps
Get a value of zero on one side of the equation.
Factor the polynomial if possible.
Apply the zero product property by setting each factor equal to zero.
Solve for the variable.

23. Solving Equations by Factoring
Definition of Quadratic Equations
Zero-Factor Property
Strategy for Solving Quadratics